Renormalization group in the infinite-dimensional turbulence: third-order results

Abstract

The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2ε) in the d-dimensional space, in connection with the problem of construction of the 1/d expansion for the fully developed fluid turbulence beyond the scope of the standard epsilon expansion. It is shown that in the large-d limit the number of the Feynman diagrams for the Green function (linear response function) decreases drastically, and the technique of their analytical calculation is developed. The main ingredients of the renormalization group approach -- the renormalization constant, beta function and the ultraviolet correction exponent omega, are calculated to order epsilon^3 (three-loop approximation). The two-point velocity-velocity correlation function, the Kolmogorov constant C_K in the spectrum of turbulent energy and the inertial-range skewness factor S are calculated in the large-d limit to third order of the epsilon expansion. Surprisingly enough, our results for C_K are in a reasonable agreement with the existing experimental estimates.

30 pages with EPS figures

References in corpus (4)

• Particles and fields in fluid turbulence
• Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation
• Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ${\epsilon }^3$
• Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field

Cited by in corpus (6)

• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• A non-perturbative renormalization group study of the stochastic Navier--Stokes equation
• Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
• Functional renormalization-group approach to decaying turbulence
• Hyperlogarithms in the theory of turbulence of infinite dimension
• Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum